- #1
zetafunction
- 391
- 0
given a set of orthogonal polynomials
[tex] \int_{-\infty}^{\infty}dx P_{m} (x) P_{n} (x) w(x) = \delta _{m,n} [/tex]
the measure is EVEN and positive, so all the polynomials will be even or odd
my question is if we suppose that for n-->oo
[tex] \frac{ P_{2n} (x)}{P_{2n}(0)}= f(x) [/tex]
for a known function f(x) can we recover the measure ??
[tex] \int_{-\infty}^{\infty}dx P_{m} (x) P_{n} (x) w(x) = \delta _{m,n} [/tex]
the measure is EVEN and positive, so all the polynomials will be even or odd
my question is if we suppose that for n-->oo
[tex] \frac{ P_{2n} (x)}{P_{2n}(0)}= f(x) [/tex]
for a known function f(x) can we recover the measure ??